Problem: Solve for $x$, $- \dfrac{3x + 4}{4x + 1} = 7$
Answer: Multiply both sides of the equation by $4x + 1$ $ -(3x + 4) = 7(4x + 1) $ $-3x - 4 = 28x + 7$ $-4 = 31x + 7$ $-11 = 31x$ $31x = -11$ $x = -\dfrac{11}{31}$